Terje Aven, University of Stavanger, NorwayPiero Baraldi, Politecnico di Milano, ItalyRoger Flage, University of Stavanger, NorwayEnrico Zio, Politecnico di Milano, Italy

• Preface ixPart I Introduction 11 Introduction 31.1 Risk 41.1.1 The concept of risk 41.1.2 Describing/measuring risk 61.1.3 Examples 61.2 Probabilistic risk assessment 81.3 Use of risk assessment: The risk management and decision-making context 111.4 Treatment of uncertainties in risk assessments 131.5 Challenges: Discussion 151.5.1 Examples 161.5.2 Alternatives to the probability-based approaches to risk and uncertainty assessment 171.5.3 The way ahead 19References – Part I 21Part II Methods 272 Probabilistic approaches for treating uncertainty 292.1 Classical probabilities 302.2 Frequentist probabilities 312.3 Subjective probabilities 352.3.1 Betting interpretation 362.3.2 Reference to a standard for uncertainty 362.4 The Bayesian subjective probability framework 372.5 Logical probabilities 393 Imprecise probabilities for treating uncertainty 414 Possibility theory for treating uncertainty 454.1 Basics of possibility theory 454.2 Approaches for constructing possibility distributions 494.2.1 Building possibility distributions from nested probability intervals 494.2.2 Justification for using the triangular possibility distribution 514.2.3 Building possibility distributions using Chebyshev’s inequality 525 Evidence theory for treating uncertainty 536 Methods of uncertainty propagation 596.1 Level 1 uncertainty propagation setting 616.1.1 Level 1 purely probabilistic framework 626.1.2 Level 1 purely possibilistic framework 646.1.3 Level 1 hybrid probabilistic–possibilistic framework 676.2 Level 2 uncertainty propagation setting 716.2.1 Level 2 purely probabilistic framework 736.2.2 Level 2 hybrid probabilistic–evidence theory framework 757 Discussion 797.1 Probabilistic analysis 807.2 Lower and upper probabilities 827.3 Non-probabilistic representations with interpretations other than lower and upper probabilities 847.4 Hybrid representations of uncertainty 857.5 Semi-quantitative approaches 87References – Part II 93Part III Practical Applications 998 Uncertainty representation and propagation in structural reliability analysis 1018.1 Structural reliability analysis 1018.1.1 A model of crack propagation under cyclic fatigue 1018.2 Case study 1028.3 Uncertainty representation 1048.4 Uncertainty propagation 1058.5 Results 1078.6 Comparison to a purely probabilistic method 1079 Uncertainty representation and propagation in maintenance performance assessment 1119.1 Maintenance performance assessment 1119.2 Case study 1139.3 Uncertainty representation 1169.4 Uncertainty propagation 1189.4.1 Maintenance performance assessment in the case of no epistemic uncertainty on the parameters 1189.4.2 Application of the hybrid probabilistic–theory of evidence uncertainty propagation method 1229.5 Results 12310 Uncertainty representation and propagation in event tree analysis 12710.1 Event tree analysis 12710.2 Case study 12810.3 Uncertainty representation 13410.4 Uncertainty propagation 13510.5 Results 13710.6 Comparison of the results to those obtained by using other uncertainty representation and propagation methods 13810.6.1 Purely probabilistic representation and propagation of the uncertainty 13810.6.2 Purely possibilistic representation and propagation of the uncertainty 13810.7 Result comparison 14110.7.1 Comparison of results 14110.7.2 Comparison of the results for the probability of occurrence of a severe consequence accident 14511 Uncertainty representation and propagation in the evaluation of the consequences of industrial activity 14711.1 Evaluation of the consequences of undesirable events 14711.2 Case study 14811.3 Uncertainty representation 15011.4 Uncertainty propagation 15211.5 Results 15211.6 Comparison of the results to those obtained using a purely probabilistic approach 15312 Uncertainty representation and propagation in the risk assessment of a process plant 15512.1 Introduction 15512.2 Case description 15512.3 The “textbook” Bayesian approach (level 2 analysis) 15612.4 An alternative approach based on subjective probabilities (level 1 analysis) 159References – Part III 163Part IV Conclusions 16713 Conclusions 169References – Part IV 173Appendix A Operative procedures for the methods of uncertainty propagation 175A.1 Level 1 hybrid probabilistic–possibilistic framework 175A.2 Level 2 purely probabilistic framework 176Appendix B Possibility–probability transformation 179Reference 181Index 183

“Therefore, I would recommend this book to a broad audience, from advanced undergraduates, to specialists, including probability theoreticians.”  (Computing Reviews, 16 July 2014)